A multi-antenna location determination (LD) system, such as the Global Positioning System (GPS) or the Global Orbiting Navigational Satellite System (GLONASS), can be used to determine attitude parameters, such as roll, pitch and yaw, of a vehicle on which antennas are located. For high accuracy measurements, carrier phase GPS signal observables should be used. Carrier phase signals have two associated signals, designated L1 and L2, with associated wavelengths of 19.03 cm and 24.42 cm, respectively. Carrier phase measurements and the problems associated with these measurements are discussed by A. Leick, GPS Satellite Surveying, John Wiley & Sons, New York, Second Edition, 1995, pp. 255-272 and 344-392. A phase observable is a difference between the phase of a received satellite carrier signal, as sensed at a receiver's antenna, and the phase of the receiver's internal oscillator. Each such phase observable will have an integer number N of cycles of radian length 2.pi. plus a fraction f of a cycle, which lies in a range 0.ltoreq.f&lt;1. The receiver will measure and report directly only the fractional cycle. Without further analysis, the integer part N of the phase observable becomes ambiguous. Resolving the integer ambiguities associated with carrier phase signals that are simultaneously received from several spaced apart satellites is a central problem in use of carrier phase signals.
Another important issue in use of carrier phase signals is determination or calibration of line biases between two or more antenna signal processing channels. The carrier phase observables needed in a multi-antenna system are the carrier phases at the phase centers of the antennas. However, the phase measurements are taken at the output terminals of phase lock loops on the GPS signal receivers. The signal transmission and processing time delay between the antenna phase centers and the phase measurement points, called line biases, need to be determined and/or eliminated.
Where two or more GPS signal-receiving antennas, having a known baseline or antenna separation vector relative to the vehicle and having known line biases, are located on the vehicle, attitude determination by carrier phase analysis is reasonably straightforward, and any of several approaches may be used. However, where one or both antennas locations are unknown and not easily determinable by standard measuring techniques, the baseline of the antennas must be determined by another approach before carrier phase analysis of the vehicle in a kinematic frame can be performed.
Double difference combinations of location determination signals, such as carrier phase measurements, have been used by some workers to remove certain errors that are common to two or more of the signal components that are part of the double differences. Examples of this work are disclosed in U.S. Pat. No. 4,912,475, issued to Counselman, U.S. Pat. No. 5,148,179, issued to Allison, U.S. Pat. No. 5,252,982, issued to Frei, U.S. Pat. No. 5,359,332, issued to Allison et al, U.S. Pat. No. 5,442,363, issued to Remondi, U.S. Pat. No. 5,451,964, issued to Babu, U.S. Pat. Nos. 5,519,620 and 5,602,741, issued to Talbot et al, U.S. Pat. No. 5,526,291, issued to Lennen, and U.S. Pat. No. 5,543,804, issued to Buchler et al. These patents disclose use of double differences but do not appear to take advantage of the separate advantages in combined use of single difference signals and double difference signals
What is needed is a single difference/double difference method, using GPS or GLONASS signals received at each of two receiver antennas from each of two transmitting satellites, for conducting a self-survey and/or a determination of signal transmission and processing line biases. Preferably, this method should not require use of any equipment not already available for GPS signal analysis and should not require use of any special orientations of the vehicle or of the vector separating the antennas.